mirror of
https://github.com/GaloisInc/cryptol.git
synced 2024-12-11 07:00:49 +03:00
146 lines
4.9 KiB
Markdown
146 lines
4.9 KiB
Markdown
Comparisons and Ordering
|
|
------------------------
|
|
|
|
(==) : {a} (Cmp a) => a -> a -> Bit
|
|
(!=) : {a} (Cmp a) => a -> a -> Bit
|
|
(===) : {a,b} (Cmp b) => (a -> b) -> (a -> b) -> a -> Bit
|
|
(!==) : {a,b} (Cmp b) => (a -> b) -> (a -> b) -> a -> Bit
|
|
|
|
(<) : {a} (Cmp a) => a -> a -> Bit
|
|
(>) : {a} (Cmp a) => a -> a -> Bit
|
|
(<=) : {a} (Cmp a) => a -> a -> Bit
|
|
(>=) : {a} (Cmp a) => a -> a -> Bit
|
|
|
|
min : {a} (Cmp a) => a -> a -> a
|
|
max : {a} (Cmp a) => a -> a -> a
|
|
|
|
instance Cmp Bit
|
|
// No instance for functions.
|
|
instance (Cmp a, fin n) => Cmp [n]a
|
|
instance (Cmp a, Cmp b) => Cmp (a, b)
|
|
instance (Cmp a, Cmp b) => Cmp { x : a, y : b }
|
|
instance Cmp Integer
|
|
|
|
Signed Comparisons
|
|
---------------------
|
|
|
|
(<$) : {a} (SignedCmp a) => a -> a -> Bit
|
|
(>$) : {a} (SignedCmp a) => a -> a -> Bit
|
|
(<=$) : {a} (SignedCmp a) => a -> a -> Bit
|
|
(>=$) : {a} (SignedCmp a) => a -> a -> Bit
|
|
|
|
// No instance for Bit
|
|
// No instance for functions.
|
|
instance (fin n, n >= 1) => SignedCmp [n]
|
|
instance (SignedCmp a, fin n) => SignedCmp [n]a
|
|
// (for [n]a, where a is other than Bit)
|
|
instance (SignedCmp a, SignedCmp b) => SignedCmp (a, b)
|
|
instance (SignedCmp a, SignedCmp b) => SignedCmp { x : a, y : b }
|
|
|
|
|
|
Arithmetic
|
|
----------
|
|
|
|
(+) : {a} (Arith a) => a -> a -> a
|
|
(-) : {a} (Arith a) => a -> a -> a
|
|
(*) : {a} (Arith a) => a -> a -> a
|
|
(/) : {a} (Arith a) => a -> a -> a
|
|
(%) : {a} (Arith a) => a -> a -> a
|
|
(^^) : {a} (Arith a) => a -> a -> a
|
|
(/$) : {a} (Arith a) => a -> a -> a
|
|
(%$) : {a} (Arith a) => a -> a -> a
|
|
lg2 : {a} (Arith a) => a -> a
|
|
negate : {a} (Arith a) => a -> a
|
|
|
|
The prefix notation `- x` is syntactic sugar for `negate x`.
|
|
|
|
// No instance for `Bit`.
|
|
instance (fin n) => Arith ([n]Bit)
|
|
instance (Arith a) => Arith ([n]a)
|
|
instance (Arith b) => Arith (a -> b)
|
|
instance (Arith a, Arith b) => Arith (a, b)
|
|
instance (Arith a, Arith b) => Arith { x : a, y : b }
|
|
instance Arith Integer
|
|
|
|
Note that because there is no instance for `Arith Bit`
|
|
the top two instances do not actually overlap.
|
|
|
|
Boolean
|
|
-------
|
|
|
|
False : Bit
|
|
True : Bit
|
|
|
|
zero : {a} (Zero a) => a
|
|
(&&) : {a} (Logic a) => a -> a -> a
|
|
(||) : {a} (Logic a) => a -> a -> a
|
|
(^) : {a} (Logic a) => a -> a -> a
|
|
complement : {a} (Logic a) => a -> a
|
|
|
|
(==>) : Bit -> Bit -> Bit
|
|
(/\) : Bit -> Bit -> Bit
|
|
(\/) : Bit -> Bit -> Bit
|
|
|
|
instance Logic Bit
|
|
instance (Logic a) => Logic ([n]a)
|
|
instance (Logic b) => Logic (a -> b)
|
|
instance (Logic a, Logic b) => Logic (a, b)
|
|
instance (Logic a, Logic b) => Logic { x : a, y : b }
|
|
// No instance for `Logic Integer`.
|
|
|
|
Sequences
|
|
---------
|
|
|
|
join : {parts,each,a} (fin each) => [parts][each]a -> [parts * each]a
|
|
split : {parts,each,a} (fin each) => [parts * each]a -> [parts][each]a
|
|
|
|
(#) : {front,back,a} (fin front) => [front]a -> [back]a -> [front + back]a
|
|
splitAt : {front,back,a} (fin front) => [from + back] a -> ([front] a, [back] a)
|
|
|
|
reverse : {n,a} (fin n) => [n]a -> [n]a
|
|
transpose : {n,m,a} [n][m]a -> [m][n]a
|
|
|
|
(@) : {n,a,m} [n]a -> [m] -> a
|
|
(@@) : {n,a,m,i} [n]a -> [m][i] -> [m]a
|
|
(!) : {n,a,m} (fin n) => [n]a -> [m] -> a
|
|
(!!) : {n,a,m,i} (fin n) => [n]a -> [m][i] -> [m]a
|
|
update : {n,a,m} (fin m) => [n]a -> [m] -> a -> [n]a
|
|
updateEnd : {n,a,m} (fin n, fin m) => [n]a -> [m] -> a -> [n]a
|
|
updates : {n,a,m,d} (fin m, fin d) => [n]a -> [d][m] -> [d]a -> [n]a
|
|
updatesEnd : {n,a,m,d} (fin n, fin m, fin d) => [n]a -> [d][m] -> [d]a -> [n]a
|
|
|
|
take : {front,back,elem} (fin front) => [front + back]elem -> [front]elem
|
|
drop : {front,back,elem} (fin front) => [front + back]elem -> [back]elem
|
|
head : {a, b} [1 + a]b -> b
|
|
tail : {a, b} [1 + a]b -> [a]b
|
|
last : {a, b} [1 + a]b -> b
|
|
|
|
groupBy : {each,parts,elem} (fin each) => [parts * each]elem -> [parts][each]elem
|
|
|
|
Function `groupBy` is the same as `split` but with its type arguments
|
|
in a different order.
|
|
|
|
Shift And Rotate
|
|
----------------
|
|
|
|
(<<) : {n,a,m} (fin n, Zero a) => [n]a -> [m] -> [n]a
|
|
(>>) : {n,a,m} (fin n, Zero a) => [n]a -> [m] -> [n]a
|
|
(<<<) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a
|
|
(>>>) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a
|
|
|
|
// Arithmetic shift only for bitvectors
|
|
(>>$) : {n, k} (fin n, n >= 1, fin k) => [n] -> [k] -> [n]
|
|
|
|
Random Values
|
|
-------------
|
|
|
|
random : {a} => [256] -> a
|
|
|
|
Debugging
|
|
---------
|
|
|
|
undefined : {a} a
|
|
error : {n a} [n][8] -> a
|
|
trace : {n, a, b} (fin n) => [n][8] -> a -> b -> b
|
|
traceVal : {n, a} (fin n) => [n][8] -> a -> a
|